Erlang-C circuit calculation, in Ruby

erlangc-circut.rb

#!/bin/ruby

#### Based on https://www.callcentrehelper.com/erlang-c-formula-example-121281.htm
#### Using ruby 2.2.0
#### I'm a pretty awful ruby programmer, so I'm sure there are a thousand ways to do this better.
#### Also, thanks StackOverflow

def erlangc_circuits(numcalls, numcalls_period, timepercall, targetanswertime, numAgentsBump)
	#integer, minutes, seconds, seconds, integer


	###Traffic Intensity: A
	callMinutes = numcalls * (timepercall/60)
	callHours = callMinutes / 60 #callHours is in Erlangs
	#puts "callHours: #{callHours}"

	###Raw number of agents required (N)
	rawNumberOfAgents = callHours + 1 + numAgentsBump
	#puts "rawNumberofAgents: #{rawNumberOfAgents}"

	###N factorial (N!)
	rawNumberOfAgentsFactorial = (1..rawNumberOfAgents).reduce(1, :*)
	#puts "rawNumberOfAgentsFactorial: #{rawNumberOfAgentsFactorial}"

	###Powers: A^N
	aToTheNPowers = callHours**rawNumberOfAgents
	#puts "A^N: #{aToTheNPowers}"

	###Simply Formula: X = (A^N)/N! * N-(N-A)
	x = (aToTheNPowers.to_f / rawNumberOfAgentsFactorial.to_f).to_f * (rawNumberOfAgents.to_f / (rawNumberOfAgents.to_f - callHours.to_f))
	#puts "x: #{x}"

	###Simplify Forumla: Y = (Sum i=0 to N-1 (A^i) / (i!))
	y = 0
	for i in 0..rawNumberOfAgents-1
		top = callHours**i
		bottom = (1..i).reduce(1, :*)

		y += (top.to_f/bottom.to_f).to_f
	end
	#puts "y: #{y}"


	###Probability call has to wait
	pw = x.to_f/(y+x).to_f
	#puts "pw: #{pw}"


	###Service Level
	targetTimeOverAHT = (targetanswertime.to_f / timepercall.to_f).to_f
	rawNumberAgentsMinusCallHours = (rawNumberOfAgents.to_f - callHours.to_f).to_f
	exp = -1 * (rawNumberAgentsMinusCallHours * targetTimeOverAHT).to_f
	serviceLevel = 1 - (pw * Math::E**(exp).to_f).to_f
	#puts "serviceLevel: #{serviceLevel}"

	return (serviceLevel * 100).to_i, rawNumberOfAgents
end


foundSolution = false
targetServiceLevel = 80
numAgentsToBump = 0.to_i
numberOfAgentsRequired = 0
while foundSolution == false
	serviceLevel, numberOfAgentsRequired = erlangc_circuits(200, 60, 180, 20, numAgentsToBump)
	#puts "#{serviceLevel} with #{numberOfAgentsRequired}"
	if (serviceLevel < targetServiceLevel)
		numAgentsToBump += 1
		foundSolution = false
	else
		foundSolution = true
	end
end
puts "#{numberOfAgentsRequired} operators required"